(1) Field of the Invention
The current invention relates to a method of signal analysis for signals of unknown duration or bandwidth.
(2) Description of the Prior Art
The formation of overlapped Hanning-weighted analysis windows is a very common first stage of processing in many time-series analysis applications. The FFT typically follows the window analysis. This is the case, for example, in the short-time Fourier transform (STFT) which is a widely used front-end for a variety of applications including automatic speech recognition (ASR). It is often necessary to arbitrarily choose an analysis window size that is a compromise between the desire for good time-domain and frequency-domain resolution. In order to handle a wide range of input time-scales, it is sometimes necessary to use multiple analysis window sizes in parallel. But this approach creates a new problem—the resolution of ambiguous results. In other words, one has to decide which FFT size is appropriate for a given input data record. A related technique is spectrogram combining where STFTs are combined in such a way that the choice of best FFT size is made at each grid point in the time and frequency plane. An important step toward solving the comparison problem is the assurance that the various SIFT representations are in some way “equivalent”. One possible definition of “equivalent” is the existence of an orthonormal linear transformation relating one analysis at a given window size to another at a different window size. This definition has relevance from a number of different viewpoints—from linear subspace analysis to statistical methods including the PDF projection theorem. See “The PDF Projection Theorem and the Class-Specific Method”, IEEE Transactions on Signal Processing, Vol. 51, No. 3 (March 2003). There is a trivial case where two analyses are related by a permutation and thus equivalent. Consider a time-series where the total number of samples T is divisible by N1 and N2. If we analyze with a rectangular window function and use no overlap between processing windows, the two analyses with window sizes N1 and N2 are permutations of the same input samples. Unfortunately, when a non-rectangular window function is used and the processing windows are overlapped, there is in general no permutation or orthonormal transformation relating the two analyses.
Thus, there is a need for a method that will allow comparisons between windowed data having different lengths when non-rectangular window functions are used.